1. Field of the Invention
The present invention relates to a method, an apparatus and a program for restoring phase information, which are used for constituting an image on the basis of image information obtained by radiation imaging or the like. In this application, the word xe2x80x9cradiationxe2x80x9d is used in a wide sense so as to include a corpuscular beam such as an electron beam, or an electromagnetic wave, in addition to a general radiation including X-rays and the like.
2. Description of a Related Art
Conventionally, an imaging method using X-rays or the like is utilized in various fields, and employed as one of the most important means for diagnosis, particularly, in a medical field. Since a first X-ray photograph was realized, X-ray photography has been repeatedly improved and a method using a combination of a fluorescent screen and an X-ray film is predominantly used at present. On the other hand, in recent years, various digitized devices such as X-ray CT, ultrasonic or MRI are in practical use and establishment of a diagnostic information processing system and the like in hospitals is being promoted. As for X-ray images, many studies have also been made for digitizing an imaging system. The digitization of the imaging system not only enables a long-term preservation of a large amount of data without incurring deterioration in image quality but also contributes to development into the medical diagnostic information system.
Incidentally, thus obtainable radiation images are generated by converting intensity of radiation transmitted through an object into brightness of the image. For example, in the case of imaging a region including a bone part, the radiation transmitted through the bone part is largely attenuated, and the radiation transmitted through a region other than the bone part, namely, a soft part is slightly attenuated. In this case, since the difference in the intensity of the radiation transmitted through different tissues is large, the radiation image with high contrast can be obtained.
On the other hand, for example, in the case of imaging a region of the soft part such as a breast, since the radiation apt to transmit wholly in the soft part, the difference between tissues in the soft part hardly appears as the difference in the intensity of the transmitted radiation. Because of this, as for the soft part, only a radiation image with low contrast can be obtained. Thus, the radiation imaging method is not suitable as a method of visualizing slight difference between tissues in the soft part.
Herein, information contained in radiation transmitted through an object includes phase information in addition to intensity information. In recent years, a phase contrast method has been studied in which an image is generated by using the phase information. The phase contrast method is an image construction technique for converting the phase difference resulted by transmitting X-rays or the like through the object into the brightness of the image.
Examples of the phase contrast method include a method of obtaining the phase difference on the basis of interference light generated by using an interferometer or a zone plate, and a method of obtaining the phase difference on the basis of diffracted light. Among them, in the method of obtaining the phase difference on the basis of the diffracted light, which method is called as a diffraction method, the phase difference is obtained on the basis of the following principle. For example, X-ray propagates through substance by travel of waves similar to light. Propagation velocity thereof varies depending on a refractive index of the substance. Therefore, when X-rays having a uniform phase are irradiated toward an object to be inspected, a difference is made in a propagation way of the X-ray, depending on the difference between tissues in the object. For this reason, a wave front of the X-ray transmitted through the object is distorted and, as a result, diffraction fringes are produced on an X-ray image obtained on the basis of the transmitted X-ray. A pattern of the diffraction fringes varies depending on the distance between a screen on which the X-ray image is formed and the object, or wavelength of the X-ray. Accordingly, by analyzing two or more sheets of X-ray images having different diffraction fringe patterns, phase difference of X-rays, which is produced at each position of the screen, can be obtained. By converting the phase difference into the brightness, the X-ray image, in which difference between tissues in the object clearly appears, can be obtained.
In particular, in the radiation transmitted through a soft part of an object, the phase difference is larger than the intensity difference depending on the difference of tissues through which the radiation has transmitted, and therefore, delicate difference between tissues can be visualized by using the phase contrast method.
For the purpose of using such a phase contrast method, imaging conditions in the radiation imaging or techniques for restoring the phase from the diffraction fringe pattern are being studied.
For example, B. E. Allman et al. xe2x80x9cNoninterferometric quantitative phase imaging with soft x raysxe2x80x9d, J. Optical Society of America A, Vol. 17, No. 10 (October 2000) pp. 1732-1743 discloses that the phase restoration is performed on the basis of image information obtained by imaging with soft X-rays to constitute an X-ray image.
In this reference, TIE (transport of intensity equation), which is the basic equation of the phase restoration, is used.                               κ          ⁢                                    ∂                              I                ⁡                                  (                                      r                    ⇀                                    )                                                                    ∂              z                                      =                              -                          ∇              ⊥                                ·                      {                                          I                ⁡                                  (                                      r                    ⇀                                    )                                            ⁢                                                ∇                  ⊥                                ⁢                                  φ                  ⁡                                      (                                          r                      ⇀                                        )                                                                        }                                              (        1        )            
where       ∇    ⊥    ⁢      =          (                        ∂                      ∂            x                          ,                  ∂                      ∂            y                              )      
and k is a wave number.
Here, principle of the phase restoration is described by referring to FIG. 8. As shown in FIG. 8, the X-ray having wavelength of xcex emits from the left side of the figure, transmits through an object plane 101 and enters a screen 102 at a distance of z from the object plane 101. At this time, when assuming intensity of the X-ray and phase thereof at a position (x,y) on the screen 102 to be I (x,y) and xcfx86 (x,y) respectively, relationship represented by the following expression holds between the intensity I (x,y) and the phase xcfx86 (x,y). Here, the intensity I is square of amplitude of the wave.                                                         2              ⁢              π                        λ                    ⁢                                    ∂                              I                ⁡                                  (                                      x                    ,                    y                                    )                                                                    ∂              z                                      =                              -            ∇                    ·                      {                                          I                ⁡                                  (                                      x                    ,                    y                                    )                                            ⁢                              ∇                                  φ                  ⁡                                      (                                          x                      ,                      y                                        )                                                                        }                                              (        2        )            
In the expression (2), by substituting k=2xcfx80 and rewriting (x,y) component into a vector r, the TIE represented by the expression (1) is derived.
Further, T. E. Gureyev et al. xe2x80x9cHard X-ray quantitative non-interferometric phase-contrast imagingxe2x80x9d, SPIE Vol. 3659 (1999) pp. 356-364, discloses that the phase restoration is performed on the basis of image information obtained by imaging with hard X-rays to constitute an X-ray image.
In this reference, the TIE represented by the expression (1) is approximated as follows.
First, the expression (1) is developed as follows:                                                                                                               -                    κ                                    ⁢                                                            ∂                                              I                        ⁡                                                  (                                                      x                            ,                            y                                                    )                                                                                                            ∂                      z                                                                      =                                  xe2x80x83                                ⁢                                                      (                                                                  ∂                                                  ∂                          x                                                                    ,                                              ∂                                                  ∂                          y                                                                                      )                                    ·                                      (                                                                                            I                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                          ⁢                                                                              ∂                                                          φ                              ⁡                                                              (                                                                  x                                  ,                                  y                                                                )                                                                                                                                          ∂                            x                                                                                              ,                                                                        I                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                          ⁢                                                                              ∂                                                          φ                              ⁡                                                              (                                                                  x                                  ,                                  y                                                                )                                                                                                                                          ∂                            y                                                                                                                )                                                                                                                          =                                  xe2x80x83                                ⁢                                                                            ∂                                              ∂                        x                                                              ⁢                                          (                                                                        I                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                          ⁢                                                                              ∂                                                          φ                              ⁡                                                              (                                                                  x                                  ,                                  y                                                                )                                                                                                                                          ∂                            x                                                                                              )                                                        +                                                            ∂                                              ∂                        y                                                              ⁢                                          (                                                                        I                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                          ⁢                                                                              ∂                                                          φ                              ⁡                                                              (                                                                  x                                  ,                                  y                                                                )                                                                                                                                          ∂                            y                                                                                              )                                                                                                                                              =                                  xe2x80x83                                ⁢                                                                            I                      ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                          (                                                                                                                                  ∂                              2                                                        ⁢                                                          φ                              ⁡                                                              (                                                                  x                                  ,                                  y                                                                )                                                                                                                                          ∂                                                          x                              2                                                                                                      +                                                                                                            ∂                              2                                                        ⁢                                                          φ                              ⁡                                                              (                                                                  x                                  ,                                  y                                                                )                                                                                                                                          ∂                                                          y                              2                                                                                                                          )                                                        +                                                                                                                          xe2x80x83                                ⁢                                                                                                    ∂                                                  I                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                                                                      ∂                        x                                                              ⁢                                                                  ∂                                                  φ                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                                                                      ∂                        x                                                                              +                                                                                    ∂                                                  I                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                                                                      ∂                        y                                                              ⁢                                                                  ∂                                                  φ                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                                                                      ∂                        y                                                                                                                                                                    =                                  xe2x80x83                                ⁢                                                                            I                      ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                                                  ∇                        2                                            ⁢                                              φ                        ⁡                                                  (                                                      x                            ,                            y                                                    )                                                                                                      +                                                            ∇                                              I                        ⁡                                                  (                                                      x                            ,                            y                                                    )                                                                                      ·                                          ∇                                              φ                        ⁡                                                  (                                                      x                            ,                            y                                                    )                                                                                                                                                        "AutoLeftMatch"                            (        3        )            
where       ∇    2    ⁢      =                            ∂          2                          ∂                      x            2                              +                        ∂          2                          ∂                      y            2                              
Further, in the expression (3), the vector r in the above document is rewritten into (x,y) components.
When the second term of the right side in the expression (3) is approximated to zero, an approximate expression represented by the following expression (4) is obtained.                                           ∂                          I              ⁡                              (                                  x                  ,                  y                                )                                                          ∂            z                          ≅                              -                                          I                ⁡                                  (                                      x                    ,                    y                                    )                                            κ                                ⁢                                    ∇              2                        ⁢                          φ              ⁡                              (                                  x                  ,                  y                                )                                                                        (        4        )            
In the expression (4), xcfx86(x,y) can be obtained from I(x,y) by a solving method such as the finite-element method.
However, in such the approximate expression (4), there is a problem that when I(x,y) has high spatial frequency components, estimated accuracy of the phase xcfx86(x,y) is deteriorated.
The present invention has been accomplished to solve the above-mentioned problems. A first object of the present invention is to provide a phase information restoring method capable of enhancing estimated accuracy of the phase upon constituting a radiation image by a phase contrast method. A second object of the present invention is to provide a phase information restoring apparatus and a phase information restoring program for performing such a phase information restoring method.
A phase information restoring method according to the present invention is a method of restoring phase information of radiation transmitted through an object on the basis of a plurality of image signals respectively obtained by detecting intensity of radiation transmitted through the object on a plurality of planes different in distance from the object, each of the plurality of image signals representing radiation image information on the plurality of planes, the method comprising the steps of: obtaining a differential signal representing difference between a first image signal and a second image signal of the plurality of image signals; subjecting any one of the plurality of image signals to one of a suppressing process and a removing process for high spatial frequency components thereof so as to generate a third image signal; obtaining Laplacian of phase with respect to the differential signal and the third image signal; and restoring phase information of the radiation by applying an inverse Laplacian operation to the Laplacian of phase.
A phase information restoring apparatus according to the present invention is an apparatus for restoring phase information of radiation transmitted through an object on the basis of a plurality of image signals respectively obtained by detecting intensity of radiation transmitted through the object on a plurality of planes different in distance from the object, each of the plurality of image signals representing radiation image information on the plurality of planes, the apparatus comprising: differential signal generating means for obtaining a differential signal representing difference between a first image signal and a second image signal of the plurality of image signals; signal processing means for subjecting any one of the plurality of image signals to one of a suppressing process and a removing process for high spatial frequency components thereof so as to generate a third image signal; phase restoring means for obtaining Laplacian of phase with respect to the differential signal and the third image signal, and restoring phase information of the radiation by applying an inverse Laplacian operation to the Laplacian of phase.
A phase information restoring program according to the present invention is a phase information restoring program for restoring phase information of radiation transmitted through an object on the basis of a plurality of image signals respectively obtained by detecting intensity of radiation transmitted through the object on a plurality of planes different in distance from the object, each of the plurality of image signals representing radiation image information on the plurality of planes, the program actuating a CPU to execute the procedures of: obtaining a differential signal representing difference between a first image signal and a second image signal of the plurality of image signals; subjecting any one of the plurality of image signals to one of a suppressing process and a removing process for high spatial frequency components thereof so as to generate a third image signal; obtaining Laplacian of phase with respect to the differential signal and the third image signal; and restoring phase information of the radiation by applying an inverse Laplacian operation to the Laplacian of phase.
According to the present invention, when phase restoration is performed by using an approximate expression on the basis of an image signal representing radiation image information obtained by X-ray imaging or the like, the image signal in which high spatial frequency components are suppressed or removed is used. Therefore, the phase restoration with high accuracy can be performed.